Estimation and Inference in Boundary Discontinuity Designs

Music City Center 

Boundary Discontinuity Designs are used to learn about treatment effects along a continuous boundary that splits units into control and treatment groups. This design corresponds to a Multi-Score Regression Discontinuity Design, a leading special case being the Geographic Regression Discontinuity Design. We study the statistical properties of local polynomial treatment effects estimators along the continuous treatment assignment boundary. We consider two distinct local polynomial methods: one based explicitly on the bivariate location variable of units relative to the treatment assignment boundary, and the other based on their univariate distance to the boundary. For each approach, we develop pointwise and uniform estimation and inference methods for the treatment effect function over the assignment boundary. We show that methods based on distance can have substantially worse misspecification biases when the boundary exhibits kinks or other irregularities. Our methods deliver valid heat maps with feasible confidence bands for treatment effects over the boundary, as well as feasible hypothesis tests of the shape of the treatment effect curve (e.g., testing for monotonic treatment effects along the boundary). We illustrate our methods with an empirical application and in simulations.

Regression discontinuity